SOLUTION: A roofer and an assistant can repair a roof together in 3 hours. Working alone, the assistant can complete the repair in 17 hours. If both the roofer and the assistant work togethe

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Question 1144431: A roofer and an assistant can repair a roof together in 3 hours. Working alone, the assistant can complete the repair in 17 hours. If both the roofer and the assistant work together for 2 hours and then the assistant is left alone to finish the job, how much longer should the assistant need to finish the repairs? (Round your answer to one decimal place.)
Found 2 solutions by richwmiller, josgarithmetic:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: Every hour the two work together, they do 1/3 of the job. So after 2 hours they have done 2/3 of the job leaving 1/3 of the job.
How long does it take the assistant to do 1/3 of the job alone?

Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
PERSON                   RATE  roofs per hours

Roofer                      1/x

Assistant                   1/17

Roofer PLUS Assistant       1/3

1%2Fx%2B1%2F17=1%2F3
51x%281%2Fx%2B1%2F17%29=%2851x%29%281%2F3%29
51%2B3x=17x
51=14x
x=51%2F14------------Roofer's rate is 14%2F51.
(This will not be needed for the question.)


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roofer and the assistant work together for 2 hours and then the assistant is left alone to finish the job, how much longer should the assistant need to finish the repairs?
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unknown time t,
%281%2F3%292%2B%281%2F17%29t=1
Solve this for t.